Select the correct pair of prepositions to fill in the blanks in the…

The correct answer is Option (4) → except, with

Prepositions in the two blanks:

• Except means apart from, leaving out.
  • First blank: the speaker wanted nothing apart from the yellow lampshade, so "anything except the yellow lampshade".
• With names the means of payment: we pay with cash, with a card or with a cheque.
  • Second blank: "pay for it with a cheque".

Complete sentence: I didn't want to buy anything except the yellow lampshade, but I didn't have enough cash and the store manager wouldn't let me pay for it with a cheque.

Why the Other Options are Incorrect?

Option 1: from, in — Incorrect.

• "Anything from the yellow lampshade" makes no sense.
• We pay in cash, but not "in a cheque".
  Example: I paid the taxi driver in cash.

Option 2: with, by — Incorrect.

• "Anything with the yellow lampshade" means something along with it, the opposite of what the speaker wants.
• "By" is used without an article (by cheque), so "by a cheque" does not fit the sentence.
  Example: You can pay the fees by cheque or online.

Option 3: besides, from — Incorrect. In a negative sentence "besides" can mean "other than", so the first blank could take it. But nobody pays "from a cheque", so the pair fails at the second blank.
Example: She has no friends here besides her cousin.

Contrast: we pay with a cheque or by cheque, but in cash.